example 4-1a from the triangle proportionality theorem, in and find su. s

From the Triangle Proportionality Theorem,

In and Find SU.

S

Answer: 15.75

In and Find BY.

B

Triangle ABC has vertices A(–2, 2), B(2, 4,) and C(4, –4). is a midsegment of Find the coordinates ofD and E.

(-2, 2)

(2, 4)

(4, –4)

Use the Midpoint Formula to find the midpoints of

Answer: D(0, 3), E(1, –1)

Triangle ABC has vertices A(–2, 2), B(2, 4) and C(4, –4).

is a midsegment of Verify that

(-2, 2)

(2, 4)

(4, –4)

slope of

If the slopes of

slope of

Answer: Because the slopes of

Triangle ABC has vertices A(–2, 2), B(2, 4) and C(4, –4).

is a midsegment of Verify that

(-2, 2)

(2, 4)

(4, –4)

First, use the Distance Formula to find BC and DE.

Answer:

Triangle UXY has vertices U(–3, 1), X(3, 3), and Y(5, –7). is a midsegment of

a. Find the coordinates of W and Z.

b. Verify that

c. Verify that

Answer: W(0, 2), Z(1, –3)

Answer: Since the slope of and the slope of

Answer: Therefore,

In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x.

Notice that the streets form a triangle that is cut by parallel lines. So you can use the Triangle Proportionality Theorem.

Answer: 32

In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x.

Answer: 5

Find x and y.

To find x:

Answer: x = 6; y = 3

Find a and b.

Answer: a = 11; b = 1.5

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